Question

If $\theta$ is the angle between two vectors $\overrightarrow{a}$ and $\overrightarrow{b}$,then $\overrightarrow{a}\cdot \overrightarrow{b}\ge 0$ only when

• A. $0<\theta <\frac{\pi }{2}$
• B. $0\le \theta \le \frac{\pi }{2}$
• C. $0<\theta <\pi$
• D. $0\le \theta \le \pi$

Answer 1

Answer: (B)

$0\le \theta \le \frac{\pi }{2}$

$\overrightarrow{a}\cdot \overrightarrow{b}\ge 0$

$\overrightarrow{a}\cdot \overrightarrow{b}=0$

if $\theta =\frac{\pi }{2}$

$\overrightarrow{a}\cdot \overrightarrow{b}=a.b\cos \theta$

$\cos \theta \in [0,1]$

$\Rightarrow 0\le \theta \le \frac{\pi }{2}$